Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#16862274 | C2 | semidirect |
| 2. C2×#16862268 | C2 | semidirect |
| 3. #22553881 | C2 | semidirect |
| 4. #22553792 | C2 | semidirect |
| 5. #22553535 | C2 | semidirect |
| 6. #22553528 | C2 | semidirect |
| 7. #22553513 | C2 | semidirect |
| 8. #22553508 | C2 | semidirect |
| 9. #22553314 | C2 | semidirect |
| 10. C2×#16862168 | C2 | semidirect |
| 11. #424×C131 | C2 | semidirect |
| 17. C2×Dic524 | C22 | semidirect |
| 19. C2×#14523502 | C22 | semidirect |
| 20. C2×#14523502 | C22 | semidirect |
| 22. C2×D1048 | C22 | semidirect |
| 28. C4×Dic262 | C22 | semidirect |
| 29. C4×D524 | C22 | semidirect |
| 34. #16862171 | C22 | semidirect |
| 37. #16862168 | C22 | semidirect |
| 41. C4⋊C8×C131 | C22 | semidirect |
| 42. C4⋊C8×C131 | C22 | semidirect |
| 47. #14523513 | D4 | semidirect |
| 154. C131 | #3045 | semidirect |
| 164. #424 | D131 | semidirect |
| 192. C4⋊C8 | C2×D131 | semidirect |
| 193. C4⋊C8 | C2×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862274 | 2 |
| C2×#16862268 | 2 |
| #22553881 | 2 |
| #22553792 | 2 |
| #22553535 | 2 |
| #22553528 | 2 |
| #22553513 | 2 |
| #22553508 | 2 |
| #22553314 | 2 |
| C2×#16862168 | 2 |
| #424×C131 | 2 |
| #3045 | 131 |